Heat broth to a simmer over medium heat. Add celery, pepper, and saffron and cook until the vegetables are softened and the broth takes on a rich color from the saffron, about 5 minutes. Bring a large pot of salted water to a boil.

Stir the chicken into the broth. Stir the noodles into the boiling water. Cook, stirring gently, until the noodles are tender, 5 to 6 minutes.

I like to mash half (or less) of a hot pepper, like a Scotch bonnet, at the bottom of each bowl. You can control the heat by the choice of pepper and by removing the seeds and ribs. Divide the noodles among the bowls and ladle the hot soup over the noodles and pepper. Sprinkle some of the chopped cilantro over each.